Curvilinear and Higher Order "edge" Finite Elements in Electromagnetic Field Computation

Summary from only given, as follows. Edge type finite elements are very useful in computation of electromagnetic fields. Unlike nodal-based finite elements, they guarantee continuity of tangential components of the field variables across element interfaces. This, in turn, eliminates the so-called spurious solutions in eigenvalue, analysis in cavities. However, most of the work in this important area is done with linear, tetrahedral elements. With the exception of a few, specially constructed elements, higher order elements do not exist because there is no systematic way of constructing such elements. A method for the systematic construction of first and second order edge and facet finite elements and their use is presented in this work. Higher order elements are also considered. Both tetrahedral and hexahedral elements am presented. These are intimately related to the corresponding nodal-based elements, allowing an easy implementation in existing nodal-based finite element computer programs. The elements constructed are then used for mode analyses in electromagnetic cavities and in eddy current calculations.